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ULTIMATE CAPACITY PREDICTION OF CARBON FIBER REINFORCED POLYMERS (CFRP)
STRENGTHENED REINFORCED CONCRETE
FLEXURAL ELEMENTS BASED ON DEBONDING FAILURE
B.C.R Jayanath,
University of Moratuwa Sri Lanka
Dr. C. S. Lewangamage,
University of Moratuwa Sri Lanka
Prof. M. T. R. Jayasinghe,
University of Moratuwa Sri Lanka
N. Prakash,
University of Moratuwa Sri Lanka
Abstract
The ultimate strength of reinforced concrete elements retrofitted in flexure by means of
externally bonded carbon fiber reinforced polymers (CFRP) has attracted the attention of
researchers due to many advantages highlighted by a wide set of experimental results. The
current paper presents analytical and experimental study on reinforced concrete (RC) flexural
elements strengthened for flexure with externally bonded CFRP. A simple yet rational model is
developed, based on cross sectional analysis, satisfying strain compatibility and equilibrium
conditions, whichis capable of predicting the ultimate moment capacity of (Fiber Reinforce
Polymers) FRP strengthened flexural sections. A total number of nine specimens, includingthree
beams, and six numbers ofone way spanning slabs were cast. One beam and three slabs were
kept as control specimens having no strengthening with CFRPand the other specimens were
strengthened with CFRP laminates and tested under the “four point loading
arrangement”.Debonding strain at the ultimate failure is calculated based on the experimental
results and compared with the existing design standards. The test results indicated that
significant enhancement of load carrying capacity can be achieved by externallyreinforced with
CFRP.
Keywords: FRP, debonding, flexure, strain
1. Introduction
Strengthening reinforced concrete (RC) structures with FRP composites is becoming an
attractive alternative for the construction industry and rehabilitation of existing concrete
structures. In particular, flexural and shear FRP reinforcing elements, externally bonded to
reinforced concrete (RC) elements constitute a larger body of the actual applications.
Reinforced concrete (RC) slabs and beams would generallyfailin flexure. However, many RC
structures could encounter shear and flexural problems due to various reasons such as mistakes
in design calculations, improper detailing of reinforcements, poor construction
practices,changing the function of a structure from lower service load to a higher service load
and reduction in or total loss of reinforcement steel area causing corrosion in service
environments etc. [1].
For strengthening shear deficient structural elements, as well as flexural strengthening,
numerous tests have been carried out [2-5] and shown that composite materials would be an
excellent option for external reinforcing. Rehabilitation of these structures can be in the form of
strengthening of structural members, repair of damaged structures or retrofitting for seismic
deficiencies. In any case, composite materials are an excellent option to be used as external
reinforcing because of their high tensile strength, light weight, resistance to corrosion and ease
of installation. Externally bonded FRP reinforcements have been shown to be applicable for the
strengthening of many types of RC structures such as columns, beams, slabs, walls, tunnels,
chimneys and silos. FRP can be usednot only to improve flexural capacity but also provides
confinement and ductility to structural members.
Number of research studies have been carried out in the recent past, to investigate the effects of
various parameters on the behavior of FRP strengthened beams and slabs in flexure [6, 7]. The
ultimate load of the strengthened RC flexural member depends principally on the compressive
strength of the concrete, the yield strength of shear and longitudinal reinforcement, the tensile
reinforcement ratio, span to depth ratio, the composite materials strength ratio, etc. Therefore, in
past research attention has been placed on performance and failure modes of FRP strengthened
flexural elements that were strengthened by using different arrangements and widths of CFRP
straps [8]. In case of flexural strengthening, bonding of CFRP at the bottom of the tension side
of the flexural element is preferred. In this way, the internal couple is increased, without
increasing the weight of the structure.
Experimental studies have shown that strengthened beams generally fail prematurely in a brittle
and sudden manner due to debonding between FRP and concrete substrate. Hence, the full
strength of the strengthening area cannot be utilized [9-11].
Based on the possible failure modes, analytical studies have been carried out to predict the
ultimate capacity of the beams. The parametric analysis conducted by An W et al [12] shows the
effect of design variables, such as external plate area, concrete compressive strength, plate
stiffness and strength and internal reinforcement ratio. It is generally assumed that the gain in
strength and stiffness are usually associated with a decrement in ductile behavior of the
structure. But it is evident that the FRP strengthened beams have shown more ductile behavior
than the RC beams and slabs.
Various analytical models have been proposed topredict the behavior of FRP strengthened
systems. Some analytical models that predict the behavior of FRP strengthened beams [13-15]
were based on iterative techniques, assuming that the beam fails in fully composite flexural
failures by either concrete crushing or rupture of the FRP laminates.
Tarek H. Almusallamand Al-Salloum [16] developed a model to predict the ultimate capacity of
FRP strengthened beams considering the balanced laminate thickness, i.e.: assuming that the
additional forces are balanced by the FRP laminates and maintain the static equilibrium at the
ultimate state.
Since the debonding failure is the most unpredictable failure mode of the FRP strengthened
structures, the criterion should be addressed with a care. The adhesion between the FRP sheet
and the concrete substrate is the most critical factor for the debonding. The design standards
follow various approaches to encounter FRP debonding failure. Practice of strength predictions
recommended by Canadian Standards Associationsuggested that the maximum allowable strain
in the FRP composite to be limited to 50% of the rupture strain. ACI-440-2R-08 [17], Japanese
standards [18] and ECP 208-2005 [19]also limit the FRP strain to certain amount to encounter the
debonding failure.
The current paper evaluate the performance, effectiveness and the modes of failure of beams,
one way spanning RC slabs strengthened with CFRP under flexure and to verify existing
debonding models for different types of strengthening schemes.A simple and efficient
computational analysis model is presented to predict the ultimate capacity of FRP strengthened
beams and slabs.
2. Experimental study
2.1 Flexural strengthening of slabs
2.1.1 Specimen details
Three slabs (125 mm × 500 mm × 1530 mm ) were singly reinforced at tension side by four
numbers of 6 mm mild steel bars (250 N/mm2) and the other two slabs were singly reinforced at
tension side by three numbers of 10 mm tor steel bars (460 N/mm2) with a concrete clear cover
of 25 mm. This corresponds to a steel reinforcement ratio of about 0.18% and 0.38%. For the
strengthened slabs, Carbon Fiber Reinforced Polymer (CFRP) strips having a width of 200 mm
and a thickness of 1 mm was bonded to the tension face of the slab with two different
arrangements, which corresponded to a CFRP reinforcement ratio of about 0.32% and 0.64%.
The slabs identifications and the details are shown in Table 1 and cross sectional details are
shown in Figures 1 to 6.
Table 1: Specimen details of slabs
Slab Dimension (mm) r/f details
height width length
Control Specimen- R6-CS1
&R6-CS2
125 500 1530 4 R6 @ 150mm
FRP bonded specimen- R6-
TS1
125 500 1530 4 R6 @ 150mm
FRP bonded specimen- R6-
TS2
125 500 1530 4 R6 @ 150mm
Control Specimen- T10-CS 125 500 1530 3 T10 @ 225mm
FRP bonded specimen- T10-
TS1
125 500 1530 3 T10 @ 225mm
500 mm
125 mm
500 mm
125 mm
200 mm
125 mm
500 mm
125 mm
500 mm
200 mm
50 mm
200 mm
200 mm
125 mm
500 mm
Figure 1: R6CS
Figure 2: R6TS1 one layer TYFO SCH41 Carbon
Strip 200mm wide.
Figure 3: R6TS2two layer TYFO SCH41
Carbon Strips 200mm wide each
Figure 4: T10CS1
Figure 5: T10TS1one layer TYFO SCH41
Carbon Strip 200mm wide
Figure 6: longitudinal section of the slabs
125 mm
3T10 or 4R6 1530 mm
Table 2:properties of FRP and composite
Typical dry fiber properties
Tensile Strength 3.79 GPa
Tensile Modulus 230GPa
Ultimate Elongation 1.7%
Density 1.74 g/cm3
Weight per sq.meter 644 g/m2
Composite gross laminate properties
Ultimate tensile strength 834MPa
Elongation at break 0.85%
Tensile Modulus 82GPa
Laminate thickness 1.00 mm
2.1.2 Testing procedure of slabs
The slabs were tested in four point bending, being simply supported on a pivot bearing on either
side over a span of 1350 mm. Identical bearing pads were placed at the loading points on top of
the beams. A spreader plate resting on top of these provided a system for load distribution. Load
was applied monotonically at the mid-span of the slab using a hydraulic jack and a loading
(proving) ring having a capacity of 100 kN. Load was applied by the increment of 5kN for the
control specimens and with the increment of 10kN for other three testing specimens. Deflection
of the slabs was noted at each load increment and the crack development was observed. Figure 7
shows a schematic diagram of a typical test specimen with loading arrangement.
2.2 Flexural strengthening of beams
2.2.1 Specimen details
Three beams having length of 2000 mm, with 200 mm × 150 mm cross section, were cast. One
beam was kept as control specimen and the other two were strengthened with CFRP. Cross
sections of the control beam and CFRP strengthened beams with the reinforcement details are
given in Figures 8 and 9.Grade 30 concrete was used for the beams and the properties of CFRP
composites are same as given in Table 2.
90 mm
Dial gauge
450 mm 450 mm 450 mm 90 mm
W
Figure 7: Loading arrangement of slabs
2.2.2 Testing procedure of beams
The beams were tested in four point bending, being simply supported on a pivot bearing on
either side over a span of 1800 mm. Identical bearing pads were placed at the loading points on
top of the beams. A spreader I-beam resting on top of these provided a system for load
distribution. Load was applied by increments of 5kN throughout the tests. Deflections were
measured at the center. The loading arrangement and the dial gauge position are shown in
Figure 10.At each load increment, locations of crack development on the concrete beams were
also noted.
Figure 10: Loading arrangement of beams
3. Flexural capacity
The experimental studies conducted on RC beams strengthened in flexure with FRP wraps,
encountered in three major failure modes: (i) classical failure of the beam. (ii) tension failure of
FRP laminate and (iii) the premature debonding failure. The classical failure corresponds to
either crushing of concrete in compression or tension failure in the steel after yielding. Tension
failure can be achieved when the FRP laminate reaches its ultimate strength. The debonding
failure occurs due to bond failure between FRP and concrete substrate.
The ultimate capacity prediction is based on a section analysis (Figure 11) The ultimate moment
capacity, Mu can be determined by taking the moment about the line in which the concrete
compression force acts and can be expressed as
(1)
Where and in which
27R6@75cc
150mm
2T10-T
2T12-B
200mm
CFRP layer
100 mm
Dial gauge
600 mm 600 mm 600 mm 100 mm
W
Figure 8: Cross section of a beam Figure 9: CFRP arrangement of the beams
ds = distance from the extreme compression fiber to the centroid of tension reinforcement
df = distance from the extreme compression fiber to the centroid of FRP reinforcement
As= area of tension steel reinforcement
Ap = area of FRP laminate
1= ratio of rectangular compression block to the depth of neutral axis
fy = yield stress of steel reinforcement
ff= the tensile stress in the FRP laminate
ffu= the ultimate tensile stress in the FRP laminate
Ef= modulus of elasticity of FRP laminate
f= the strain in the FRP laminate, corresponding to ff
fd=debonding strain of FRP
The ultimate moment of the section can be determined by an iterative procedure. According to
FRP strain at failure, concrete strain c, and steel strain s, are determined using equations 2 and
3.
When debonding occurs, FRP strain at failure f = fd
(2)
(3)
Based on the strain values, the compressive force in concrete (C), tensile force in FRP laminates
(Tp) and tensile force in steel (Ts) can be calculated and the static equilibrium is verified by
adjusting the value of a.
Steel stress at failure fs, and stress in the FRP laminates ff, can be expressed in terms of strains
(equations 4 and 5).
Figure 11: Stress and strain across the depth of a FRP strengthened section
f’c
c b
h ds df
c a=1c
f’c
As
Af f
s>y
N.A
C
Ts= Asfy
Tp= Afff
(4)
(5)
Ratio of the rectangular compression block to the depth of neutral axis is calculated from
equation 6, which given in ACI 318M-08[20].
(6)
The existing debonding criteria for the calculation are listed below.
ACI 440.2R-08:
Where, CEis the environmental reduction factor which can be taken as 0.95, is the ultimate
strain of FRP, is the debonding strain of FRP, f’c is the concrete compressive strength, n is the
number of FRP plies, Ef is the modulus of elasticity of FRP material and tfis the thickness of the
FRP layer.
The Egyptian code ECP 208-2005:
Where, feis the effective FRP strain, n is the number of plies,Ef is the modulus of elasticity of
FRP material and tfis the thickness of the FRP layer.
Japanese standard
Where Gf is the interfacial fracture energy between FRP and concrete and its value can be taken
as 0.5 N/mm2.
4. Results and validation
4.1 Slabs
Data gathered from experimental programmearesummarized in table 3, in terms of failure load
and the failure mode.
Table 3: Failure loads and failure modes of beams.
Slab Failure load (kN)
Failure mode
Control Specimens R6-CS1 18.24 Concrete crushing
R6-CS2 18.21
FRP bonded specimen-
R6-TS1
48.56 CFRP debonding
FRP bonded specimen-
R6-TS2
85.61 CFRP debonding
Control Specimen-
T10-CS
29.17 Concrete crushing
FRP bonded specimen-
T10-TS1
82.16 CFRP debonding
Control specimens were failed in steel yielding and concrete crushing. Flexural cracks were
observed during the failure (Figures 12 and 13).
Figure 12: Crack propagation of R6-CS1
The FRP strengthened slabs were failed in FRP debonding and concrete crushing, resulting a
brittle type failure. The FRP laminates were separated from the concrete surface without
rupture, (Figure 14)
Figure 13: Crack propagation T10-CS1
Load vs. deflection relationships of the specimens are shown in figures 10 and 11.
Figure 16: Load Vs Deflection curve of the mid span of the slabs for T10CS1 and T10TS1
0
10
20
30
40
50
60
70
80
90
0 2 4 6 8 10
Load
(k
N)
deflection at mid span (mm)
R6-CS R6-TS1 R6-TS2
Figure 14: Debonding failure of FRP strengthened slabs
Figure 15: Load Vs Deflection curve of the mid span of the
slabs for R6CS, R6TS1 and R6TS2
0
10
20
30
40
50
60
70
80
90
0 5 10 15
load
(k
N)
deflection at mid span (mm)
T10-CS1 T10-TS1
It was observed that nearly 150 % strength increment could be achieved in this particular case.
The predicted moment capacities by using the values of debonding strain, proposed by the
guidelines and the experimental moment capacities of the slabs are compared in Table 4.
Table 4 Comparison of predicted ultimate moment capacities with experimental values
Specimen Predicted ultimate moment capacity (kNm) Experimentally
(kNm) ACI 440-2R-08 Japanese
standards
Egyptian
codeECP 208-
2005 R6TS1 17.25 9.80 17.99 10.92
R6TS2 31.01 16.69 32.42 19.26
T10TS1 24.56 17.24 25.29 18.48
4.2 Beams
Data gathered from experimental programmearesummarized in table 5, in terms of failure load
and the failure modeSummary of the failure loads and the failure modes are given in Table 5.
Table 5: Comparison of failure loads in beams
Beam Experimental
Failure load (kN)
Failure mode
Control Specimen 66 Concrete crushing
CFRP bonded specimen-01(TB1) 120 Concrete crushing and CFRP debonding
CFRP bonded specimen-02(TB2) 123 CFRP debonding
Figure 17shows the flexural cracks propagation on the control specimen and Figure 18 shows
the failure mode of the CFRP bonded specimens.
Figure 17: Flexural cracks in control beam Figure 18: Debonding failure of FRP
strengthened beam
Deflection pattern of the CFRP strengthened beams were almost the same and failure load was
doubled compare to the control specimen. Figure 19shows the Load Vs. Deflection of the mid
span.
It was observed that nearly 84% strength increment could be achieved in this particular case.
The predicted moment capacities by using the values of debonding strain, proposed by the
guidelines and the experimental moment capacities of the beams are compared in table 6.
Table 6: Comparison of predicted ultimate moment capacities withexperimental values
Specimen Predicted ultimate moment capacity (kNm) Experimntally(kNm)
ACI 440-2R-08 Japanese
standards
Egyptian
codeECP 208-
2005 TB1 38.83 28.15 39.87 36.00
TB2 38.83 28.15 39.87 36.90
Table 7summarizes the debonding strains which were calculated by using, ACI 440-2R-08,
Japanese standards, Egyptian standards and compared with the strain values calculated based on
the experimental results.
-5
5
15
25
35
45
55
65
75
85
95
105
115
125
0 5 10 15 20 25 30
Lo
ad
(k
N)
Deflection (mm)Deflection of the control specimen (mm)Deflection of the test specimen-01 (mm)Deflection of the test specimen-02 (mm)
Figure 19: Load Vs deflection curve of the mid span of the beams
Table 7: Comparison of debonding strain values
The bonding stresses of CFRP-concrete interface are mainly shear and normal stresses. CFRP
on bottom of the beams and the slabs, which are used for flexural strengthening, carries tensile
stresses transferred through interface shear stresses and improves the bending load carrying
capacity of the structural elements. The interface bonding also has influence on strengthened
flexural behavior. At the end part of CFRP where there is a truncation of FRP, stress
concentrations occurred which leads to the CFRP de-bonding.
As predicted by the existing guide lines, debonding strain at the failure was calculated and
compared with the debonding strain values calculated by using the experimental results. The
comparison of the results given in Table 7 show that the variation of the results.
5. Conclusion
The structural performance of RC beams and slabs strengthened with CFRP sheets has been
evaluated. The flexural tests carried out in this study demonstrated that external bonding of
CFRP sheets is an effective technique of strengthening. The experimental results showed that
the CFRP bonded with epoxy could effectively improve the structural performance of RC
beams by increasing both the load carrying capacity and the corresponding ductility compared
with unstrengthened RC beams.
The experimental results show that the actual debonding strain at failure cannot be predicted
according to existing guidelines. Hence, further experimental and theoretical studies will be
carried out to identify and understand the complete behaviour of CFRP strengthened flexural
elements under tropical climatic conditions.
Specimen Debonding strain at ultimate failure
From experiment ACI 440-2R-08 Japanese
standards
Egyptian code
ECP 208-2005
R6TS1 0.00415 0.00727 0.00349 0.00765
R6TS2 0.00415 0.00727 0.00349 0.00765
T10TS1 0.00415 0.00727 0.00349 0.00765
TB1 0.00625 0.00726 0.00349 0.00765
TB2 0.00625 0.00726 0.00349 0.00765
Acknowledgment
This research is supported by University of MoratuwaSenate Research Grant (Grant no
SRC/LT/2011/26). The authors are grateful to Mr.DhammikaWimalarathne who provided the
FRP materials for the research.
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